MathDB

10

Part of 2024 AIME

Problems(2)

Olympiad Geometry on AIME yay

Source:

2/2/2024
Let △ABC\triangle ABC have side lengths AB=5,BC=9,AB = 5, BC = 9, and CA=10.CA = 10. The tangents to the circumcircle of △ABC\triangle ABC at BB and CC intersect at point D,D, and AD‾\overline{AD} intersects the circumcircle at P≠A.P \ne A. The length of AP‾\overline{AP} is equal to mn,\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+n.m + n.
geometryAMCAIME
2019 CIME I/14 moment

Source: 2024 AIME II #10

2/8/2024
Let △ABC\triangle ABC have circumcenter OO and incenter II with IA‾⊥OI‾\overline{IA}\perp\overline{OI}, circumradius 1313, and inradius 66. Find AB⋅ACAB\cdot AC.
AMCAIMEAIME II